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Parikh vectors
5UDX_1 6SLV_1 8BXA_1 Letter Amino acid
6 5 2 P Proline
22 14 9 D Aspartic acid
9 7 5 Q Glutamine
13 29 10 E Glutamic acid
15 5 4 F Phenylalanine
19 19 6 S Serine
3 2 0 W Tryptophan
8 10 3 Y Tyrosine
33 24 4 A Alanine
18 13 8 R Arginine
17 7 6 N Asparagine
4 3 1 H Histidine
1 2 0 C Cysteine
8 10 9 I Isoleucine
20 10 5 T Threonine
19 12 8 V Valine
17 14 6 G Glycine
32 24 10 L Leucine
15 17 12 K Lycine
7 9 8 M Methionine 

5UDX_1|Chains A, B, C, D, E, F|Lactate racemization operon protein LarE|Lactobacillus plantarum (strain ATCC BAA-793 / NCIMB 8826 / WCFS1) (220668)
>6SLV_1|Chain A|14-3-3 protein sigma|Homo sapiens (9606)
>8BXA_1|Chain A|Ribosome-binding factor A|Staphylococcus aureus subsp. aureus NCTC 8325 (93061)
Protein code \(c\) LZ-complexity \(\mathrm{LZ}(w)\) Length \(n=|w|\) \(\frac{\mathrm{LZ}(w)}{n /\log_{20} n}\) \(p_w(1)\) \(p_w(2)\) \(p_w(3)\) Sequence \(w=f(c)\)
5UDX , Knot 121 286 0.79 40 169 267 
MATLATKKATLVAALKDLQRVTVAFSGGIDSTLVLKMALDVLGRDNVTAVVANSELFTDEEFDKAMSLAEELGANVQGTTLDYLSDDHIKNNTPDSWYYAKKMFYSRLNDIAANNGSAAVLDGMIKNDENDYRPGLKARSEAGARSLLQEADFFKTDVRALAQELGLTNWNKVASCSVSSRFPYGTTLTHDNIAQVMAAEKYLRSLGFPTVRVRFHNDIARIELPEARIGDFLVFNDRVNRQLQSLGFRYVTLDLGGFRSGRMNDTLTKAQLATFAASWSHPQFEK
6SLV , Knot 108 236 0.83 40 164 229 
GAMGSMERASLIQKAKLAEQAERYEDMAAFMKGAVEKGEELSCEERNLLSVAYKNVVGGQRAAWRVLSSIEQKSNEEGSEEKGPEVREYREKVETELQGVCDTVLGLLDSHLIKEAGDAESRVFYLKMKGDYYRYLAEVATGDDKKRIIDSARSAYQEAMDISKKEMPPTNPIRLGLALNFSVFHYEIANSPEEAISLAKTTFDEAMADLHTLSEDSYKDSTLIMQLLRDNLTLWT
8BXA , Knot 54 116 0.73 36 89 111 
MSSMRAERVGEQMKKELMDIINNKVKDPRVGFITITDVVLTNDLSQAKVFLTVLGNDKEVENTFKALDKAKGFIKSELGSRMRLRIMPELMYEYDQSIEYGNKIERMIQDLHKQDR

Let \(P_w(n)\) be the set of distinct subwords (intervals) in a word \(w\). Let \(p_w(n)\) be the cardinality of \(P_w(n)\). Let \(f(c)\) be the sequence in FASTA with 4-symbol Protein Data Bank code \(c\).

\(|P_{f(5UDX_1)}(2) \setminus P_{f(6SLV_1)}(2)|=75\), \(|P_{f(6SLV_1)}(2) \setminus P_{f(5UDX_1)}(2)|=70\). Let \( Z_k(x,y)=|P_x(k)\setminus P_y(k)|+|P_y(k)\setminus P_x(k)| \) be a LZ76 style (set of subwords) Jaccard distance numerator for \(P(k)\).Hydrophobic-polar version of Sequence 1:1101100010111110010010111011100011101110111000101111000110000100110110011101010010010000100001001001001100010011100101111011100000000111010001110011001011000101110011100100110001000110100100001101111000100111101010100011010110101101111000100010011100101011110010100010010110111010010100
Pair \(Z_2\) Length of longest common subsequence
5UDX_1,6SLV_1 145 4
5UDX_1,8BXA_1 160 3
6SLV_1,8BXA_1 145 4

Newick tree

 
[
	8BXA_1:77.58,
	[
		5UDX_1:72.5,6SLV_1:72.5
	]:5.08
]

Let d be the Otu--Sayood distance d.
Let d1 be the Otu--Sayood distance d1. (This makes the 4TYN sequence AAAAAA a close match...)
A roughly speaking expected distance is \((0.85)(0.8)(\frac{522 }{\log_{20} 522}-\frac{236}{\log_{20}236})=81.9\)
Status Protein1 Protein2 d d1/2
Query variables 5UDX_1 6SLV_1 102 93.5
Was not able to put for d
Was not able to put for d1

In notation analogous to [Theorem 16, Kjos-Hanssen, Niraula and Yoon (2022)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]